Meaningful Access to Federal Health Plan Claims Data Act of 2021 This bill requires the Centers for Medicare & Medicaid Services (CMS) to establish a program that allows clinician-led clinical data registries to access Medicare claims data for purposes of research, quality of care measurement, and reporting. (Clinician-led clinical data registries are data repositories operated by clinician organizations and that collect information about particular diseases and related medical procedures and therapies.) The new program must allow for various types of data queries, including provider, state, and nationwide claims data. Such data may be used for public reports about provider performance, specified nonpublic analyses (e.g., medical research), and fee-based data services. Registries must apply to the CMS for access. Additionally, registries and their authorized users must enter into data use agreements and are subject to monetary penalties for breaching such agreements. The bill also allows for Medicare coverage of new and emerging items and services for purposes of evidence collection in relation to such items and services.